(Solved): Consider a ceiling fan with a moment of inertia I about its axis of rotation. The fan is turned by a ...

Consider a ceiling fan with a moment of inertia I about its axis of rotation. The fan is turned by an applied torque and rotates in a lubricated bearing with viscous coefficient b. The fan’s angular velocity is w(t).  

Consider a ceiling fan with moment of inertia I about its axis of rotation. The fan is turned by an applied torque T(t) and rotates in a lubricated bearing with viscous coefficient b. The fan's angular velocity is wo(t). 1. The fan's initial angular velocity is zero. Beginning at t=0, the fan is sub- jected to a constant torque T, (given), so that the fan's motion is (t)=(1-e). The fan's initial acceleration (given) is a.. At some time after the fan has reached steady state, the applied torque suddenly drops to zero. At a time 4t (given) after the torque drops to zero, the angular veloci- ty has decreased by N% (given). Solve for I and in terms of given quanti- ties. 2. The viscous coefficient of the bearing is b (given). Propelled by a constant torque T (given), the fan is moving with constant angular velocity , (giv- en) in the + direction when an angular impulse (impulsive torque) Î (giv- en) is applied at t=0 in the - direction. Immediately after the impulse, the block's angular velocity is ? (given) in the - direction. The constant torque T, continues to be applied, so that the fan's angular velocity after the impulse is w(t)=-we+*+w0? ( e*² +0,{(1-e*). Solve for I and the time when the fan reverses direction in terms of given quantities.